Abstract
Our problem is to decompose a positive dimensional solution set of a polynomial system into irreducible components. This solution set is represented by a witness set, which can be partitioned into irreducible subsets according to the action of monodromy. Our straightforward parallel version of the original monodromy breakup algorithm suffers from synchronisation issues. The new approach not only resolves these issues, but also, according to accumulated statistics, reduces the expected number of homotopy continuation paths tracked. The latter property gives a faster serial algorithm.
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